Baire classes of Banach spaces and strongly affine functions

Spurný, Jiří

doi:10.1090/S0002-9947-09-04841-7

Baire classes of Banach spaces and strongly affine functions
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Trans. Amer. Math. Soc. 362 (2010), 1659-1680 Request permission

Abstract:

We construct a metrizable simplex $X$ and a Baire–two function $f$ on $X$ satisfying the barycentric formula such that $f$ is not of affine class two; i.e., there is no bounded sequence of affine Baire–one functions on $X$ converging to $f$. This provides an example of a Banach $\mathcal {L}_\infty$–space $E$ such that $E_{2}^{**}\neq E_{\mathcal {B}_2}^{**}$.

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